A scientific theory is an explanation that
1 answer:
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Answer:
v_{1fy} = - 0.4549 m / s
Explanation:
This is an exercise of conservation of the momentum, for this we must define a system formed by the two balls, so that the forces during the collision have internal and the momentum is conserved
initial. Before the crash
p₀ = m v₁₀
final. After the crash
= m
+ m v_{2f}
Recall that velocities are a vector so it has x and y components
p₀ = p_{f}
we write this equation for each axis
X axis
m v₁₀ = m v_{1fx} + m v_{2fx}
Y Axis
0 = -m v_{1fy} + m v_{2fy}
the exercise tells us the initial velocity v₁₀ = 1.83 m / s, the final velocity v_{2f} = 1.15, let's use trigonometry to find its components
sin 23.3 = v_{2fy} / v_{2f}
cos 23.3 = v_{2fx} / v_{2f}
v_{2fy} = v_{2f} sin 23.3
v_{2fx} = v_{2f} cos 23.3
we substitute in the momentum conservation equation
m v₁₀ = m v_{1f} cos θ + m v_{2f} cos 23.3
0 = - m v_{1f} sin θ + m v_{2f} sin 23.3
1.83 = v_{1f} cos θ + 1.15 cos 23.3
0 = - v_{1f} sin θ + 1.15 sin 23.3
1.83 = v_{1f} cos θ + 1.0562
0 = - v_{1f} sin θ + 0.4549
v_{1f} sin θ = 0.4549
v_{1f} cos θ = -0.7738
we divide these two equations
tan θ = - 0.5878
θ = tan-1 (-0.5878)
θ = -30.45º
we substitute in one of the two and find the final velocity of the incident ball
v_{1f} cos (-30.45) = - 0.7738
v_{1f} = -0.7738 / cos 30.45
v_{1f} = -0.8976 m / s
the component and this speed is
v_{1fy} = v1f sin θ
v_{1fy} = 0.8976 sin (30.45)
v_{1fy} = - 0.4549 m / s
Answer:
(i) See attached image for the drawing
(ii) net force given in component form: (20, 20)N with magnitude:
Explanation:
First try to write all forces in vector component form:
The force F1 acting at 45 degrees would have multiplication factors of on both axes, to take care of the sine and cosine projections. Therefore, the:
x-component of F1 is
y-component of F1 is
As far as force F2, it is given already in x and y components, then:
x-component of F2 = 8 N
y-component of F2 = -6 N (negative meaning pointing down the y-axis)
Force F3 has only component (upwards) in the y-direction
x-component of F3 = 0 N
y-component of F3 =14 N
The additions of all these component by component, gives the resultant force (R) acting on the 5 kg mass:
x-component of R = 12 + 8 = 20 N
y-component of R = 12 + 14 - 6 = 20 N
Therefore, the acceleration that the mass receives due to this force is given in component form as:
x-component of acceleration: 20 N / 5 kg =
y-component of acceleration: 20 N / 5 kg =
Now we can calculate the components of the velocity of this mass after 2 seconds of being accelerated by this force, using the formula of acceleration times time:
x-component of the velocity is:
y-component of the velocity is:
